A partly paid share is a share in a company which has only partial been paid compared to the par value, with the understanding that as the company requires more funds, calls will be made from time to time to request more money until the shares are fully paid, when no further calls can be made.
The amounts may be specified in the prospectus or unspecified, and the shareholder is liable when a call is made by the company until the shares are fully paid.
This was good for the financial institution as they could quickly increase their capital when required but was unpopular with shareholders as they had an unknown liability that could be called upon at any time and for this reason the practice largely died out.
[1] Calls on partly paid shares may be made in accordance with a schedule of calls set out in the company's original prospectus or it may be made at the discretion of the directors.
The obligation falls on the owner at the time of a call, who may have disposed of the shares by the time payment is due, so that the new owner is free of the obligation to pay the call.